Question

Boy oh boy, guess what? More sums!

Answer 1

I know that the sum of \[\sum_{k=0}^{\infty}\frac{ 2 }{ 5^k }=\frac{ 5 }{ 2 }\]. My question is how do you find the sum of \[\sum_{k=2}^{\infty}\frac{ 2 }{ 5^k }?\]

Answer 2

why not break things up

\[\LARGE \sum_{k=0}^{\infty}\frac{2}{5^k}=\sum_{k=0}^{k=1}\frac{2}{5^k} + \sum_{k=2}^{\infty}\frac{2}{5^k}\]

Answer 3

That's just it though. I do actually want to understand how the problem works. And...yes! I ended up splitting it to solve it!